Two congruent isosceles triangles and three lines. Prove triangle AEF is also isosceles.

Solution

Triangles ABD and CBE are similar since they are both isosceles and they have the same top angle at vertex B. Therefore also ∠EAF equals ∠AEF and hence △AEF is isosceles.

An interesting finding by Ignacio Larrosa Cañestro is that the locus of point F seems to be a hyperbola.

Poem

The fallen pine
the tree is sad
he is just be cut
by human hands
like a giant
his crown to earth
he is broken and dirty
no more rain
no more life
no more thunder
just a yearning
just a burning
a windswept pine tree
when the pine tree fell
just a big sadness

Bella